Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}4x-6y &= -7 \\ 4x-3y &= 2\end{align*}$
Solution: Begin by moving the $x$ -term in the second equation to the right side of the equation. $-3y = -4x+2$ Divide both sides by $-3$ to isolate $y$ $y = {\dfrac{4}{3}x - \dfrac{2}{3}}$ Substitute this expression for $y$ in the first equation. $4x-6({\dfrac{4}{3}x - \dfrac{2}{3}}) = -7$ $4x - 8x + 4 = -7$ Simplify by combining terms, then solve for $x$ $-4x + 4 = -7$ $-4x = -11$ $x = \dfrac{11}{4}$ Substitute $\dfrac{11}{4}$ for $x$ back into the top equation. $4( \dfrac{11}{4})-6y = -7$ $11-6y = -7$ $-6y = -18$ $y = 3$ The solution is $\enspace x = \dfrac{11}{4}, \enspace y = 3$.